Question

If f(s)=f(t) then s=t true or false and why

Answer 1

hint: think of a parabola (and its symmetry)

Answer 2

It's false

Answer 3

it is false in general.

Answer 4

your statement should be
"For any function f , if f(s) = f(t) then s = t ."

This is false because you can produce a counterexample
Suppose we look at the function f(x) = x^2 , R -> R
Now f(-2) = f(2) = 4 so the hypothesis is true f(s) = f(t)
but -2 =/= 2 so the conclusion is false ( s not equal to t)

Answer 5

so we showed it is false that for any function f , when f(s) = f(t) then s = t .
We found a function where f(s) = f(t) , but s is not equal to t

Answer 6

There are some function for which the statement is true , these functions are called 1 to 1 functions. But in general it is false (it is not true for all functions).